Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8667)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.8667.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(5/2), -(23/4)}, -z] == (1/(476974575 z^(1/4))) (Sqrt[2] ((476974575 + 1128148560 z + 718336080 z^2 + 98638848 z^3 + 47738880 z^4 - 13762560 z^5 + 1048576 z^6) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (158991525 + 164060820 z - 19681200 z^2 + 7666176 z^3 - 1835008 z^4 + 131072 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (476974575 - 143783640 z + 11531520 z^2 + 14773248 z^3 - 3637248 z^4 + 262144 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]